Abstract

A new efficient algorithm is presented for joint diagonalization of
several matrices. The algorithm is based on the Frobenius-norm
formulation of the joint diagonalization problem, and addresses
diagonalization with a general, non-orthogonal transformation. The
iterative scheme of the algorithm is based on a multiplicative update
which ensures the invertibility of the diagonalizer. The algorithm s
efficiency stems from the special approximation of the cost function
resulting in a sparse, block-diagonal Hessian to be used in the
computation of the quasi-Newton update step. Extensive numerical
simulations illustrate the performance of the algorithm and provide a
comparison to other leading diagonalization methods. The results of such
comparison demonstrate that the proposed algorithm is a viable
alternative to existing state-of-the-art joint diagonalization
algorithms. The practical use of our algorithm is shown for blind source
separation problems.